A train with oi120 wagons crosses Arjun who is going in the same direction in 36 seconds. It travels for half an hour from the time it started overtaking the arjun ( he is riding on the horse ) before it starts overtaking srikrishana ( who is also riding on his horse ) coming from the opposite direction in 24 seconds. in how much time ( in seconds) after the train has crossed the srikrishna do the Arjun meets to srikrishna?

Options

A. 3560 sec
B. 3600 sec
C. 3576 sec
D. can't be determined

Answer

To solve the problem step by step, we will break down the information provided and calculate the required time for Arjun and Srikrishna to meet after the train has crossed Srikrishna.

### Step 1: Understanding the Problem
- A train with 120 wagons crosses Arjun in 36 seconds.
- The train travels for half an hour (30 minutes) before it starts overtaking Srikrishna, who is coming from the opposite direction, and this takes 24 seconds.
- We need to find the time in seconds after the train has crossed Srikrishna when Arjun meets Srikrishna.

### Step 2: Determine the Speed of the Train
Let the length of the train be \( L \) and the speed of the train be \( U \). The time taken to cross Arjun is given as 36 seconds.

Using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
The distance covered by the train while crossing Arjun is equal to the length of the train \( L \):
\[ L = U \times 36 \]

### Step 3: Determine the Speed of Srikrishna
Let the speed of Srikrishna be \( V \). The train crosses Srikrishna in 24 seconds. Thus, we can write:
\[ L = (U + V) \times 24 \]

### Step 4: Set Up the Equations
From the two equations we have:
1. \( L = U \times 36 \)
2. \( L = (U + V) \times 24 \)

Setting these equal gives:
\[ U \times 36 = (U + V) \times 24 \]

### Step 5: Simplify the Equation
Expanding the second equation:
\[ U \times 36 = U \times 24 + V \times 24 \]
Rearranging gives:
\[ U \times 36 - U \times 24 = V \times 24 \]
\[ U \times (36 - 24) = V \times 24 \]
\[ 12U = 24V \]
Thus, we can simplify to find the relationship between \( U \) and \( V \):
\[ V = \frac{1}{2}U \]

### Step 6: Calculate the Distance Between Arjun and Srikrishna
The train travels for half an hour (30 minutes) before it starts overtaking Srikrishna. The distance traveled by the train in this time is:
\[ \text{Distance} = U \times 30 \times 60 = 1800U \]

### Step 7: Calculate the Time for Arjun and Srikrishna to Meet
The distance between Arjun and Srikrishna when the train starts crossing Srikrishna is:
\[ \text{Distance} = 1800U \]
The relative speed of Arjun and Srikrishna is:
\[ V - U = \frac{1}{2}U - U = -\frac{1}{2}U \]
Since they are moving towards each other, we take the absolute value:
\[ \text{Relative Speed} = U + \frac{1}{2}U = \frac{3}{2}U \]

The time taken for Arjun and Srikrishna to meet is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{1800U}{\frac{3}{2}U} = \frac{1800 \times 2}{3} = 1200 \text{ seconds} \]

### Step 8: Adjust for the Time Taken by the Train to Cross Srikrishna
After the train crosses Srikrishna in 24 seconds, the time for Arjun and Srikrishna to meet is:
\[ \text{Final Time} = 1200 - 24 = 1176 \text{ seconds} \]

### Final Answer
The time in seconds after the train has crossed Srikrishna when Arjun meets Srikrishna is **1176 seconds**.